I began Googling around for an easy way to do this, and I quickly found this great tip on Spanish Only. Let me lay out the [sarcasm] long, complicated [/sarcasm] process for you. It goes like this:

Copy the URL of your audio file.

Paste the URL of the audio file into an Anki field.

Yes, that is all you need to do. Anki will then do all the heavy lifting, first converting the URL into an Anki-friendly text string and then downloading the file so you have it sitting on your computer.

So where do you get those audio files? You haven't already forgotten yet about RhinoSpike, have you? Here's a list of all of my audio requests on RhinoSpike. Most of those posted yesterday are the vocabulary words from a Japanese article I read. Click on the "Listen" button next to any of those requests, and you'll get a list of recordings. Next to each recording is an "MP3" button. Click that, and you've got your URL, ready to copy and paste into Anki.